Thanks a lot for sharing the characters/stages and your investigations into what is going wrong! I'll take a look and let you know what I find. Can't really say why it's going wrong, it might be because Dolmexica internally assumes 4:3 resolutions for doing its coordinate system conversions, I imagine that breaks all over the place, I'll have to step through everything to see why it's going so poorly.
The sprite transparency issue might be some unsupported format like I mentioned before, maybe something related to palettes in the more modern .sff formats, I think Dolmexica struggled with them sometimes. I'll also let you know what I find there.
Thanks a lot again for taking the time to share what you found and the files!